{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第八次 换手率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np #数据处理最重要的模块\n",
    "\n",
    "import pandas as pd#数据处理最重要的模块\n",
    "\n",
    "import scipy.stats as stats #统计模块\n",
    "\n",
    "import scipy\n",
    "\n",
    "# import pymysql# 导入数据库模块\n",
    "\n",
    "\n",
    "from datetime import datetime #时间模块\n",
    "\n",
    "import statsmodels.formula.api as smf # OLS regression\n",
    "\n",
    "#import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "\n",
    "import matplotlib.pyplot as plt #画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties #作图中文\n",
    "from pylab import mpl\n",
    "\n",
    "#mpl.rcParam['font.sans-serif']= ['imHei' ]\n",
    "\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "#输出矢量图，渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "from IPython.core.interactiveshell import InteractiveShell #jupter运行输出的模块\n",
    "#显示，每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity='all'\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "#设置不限制数量\n",
    "pd.set_option('display.max_columns',None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1987-01-31</th>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-02-28</th>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-03-31</th>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-04-30</th>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-05-31</th>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>453 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            cpi\n",
       "month          \n",
       "1987-01-31  5.1\n",
       "1987-02-28  5.4\n",
       "1987-03-31  5.8\n",
       "1987-04-30  6.7\n",
       "1987-05-31  7.6\n",
       "...         ...\n",
       "2024-05-31  0.3\n",
       "2024-06-30  0.2\n",
       "2024-07-31  0.5\n",
       "2024-08-31  0.6\n",
       "2024-09-30  0.4\n",
       "\n",
       "[453 rows x 1 columns]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inflation=pd.read_csv('datasets/inflation.csv')\n",
    "inflation['month']=pd.to_datetime(inflation['month'],format='%Y/%m/%d')\n",
    "inflation.set_index('month',inplace=True)\n",
    "inflation.sort_values(by=['month'],axis=0,ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "      <td>126000.00</td>\n",
       "      <td>4.940000e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "      <td>19700.00</td>\n",
       "      <td>8.400000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "      <td>2800.00</td>\n",
       "      <td>1.600000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "      <td>3200.00</td>\n",
       "      <td>3.100000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "      <td>1500.00</td>\n",
       "      <td>6.000000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8251 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980    126000.00   \n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390     19700.00   \n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130      2800.00   \n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550      3200.00   \n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250      1500.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  \n",
       "Day                       \n",
       "1990-12-19  4.940000e+05  \n",
       "1990-12-20  8.400000e+04  \n",
       "1990-12-21  1.600000e+04  \n",
       "1990-12-24  3.100000e+04  \n",
       "1990-12-25  6.000000e+03  \n",
       "...                  ...  \n",
       "2024-09-24  4.427953e+07  \n",
       "2024-09-25  5.166981e+07  \n",
       "2024-09-26  5.246691e+07  \n",
       "2024-09-27  4.806126e+07  \n",
       "2024-09-30  1.167773e+08  \n",
       "\n",
       "[8251 rows x 7 columns]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=pd.read_csv('000001.csv') #'datasets/000001.csv'\n",
    "data['Day']=pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day',inplace=True)\n",
    "data.sort_values(by=['Day'],axis=0,ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>23451800.00</td>\n",
       "      <td>1.806930e+08</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>42222000.00</td>\n",
       "      <td>3.069230e+08</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>43012300.00</td>\n",
       "      <td>3.015330e+08</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>48748200.00</td>\n",
       "      <td>3.537580e+08</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>50985100.00</td>\n",
       "      <td>3.985190e+08</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880  23451800.00   \n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810  42222000.00   \n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890  43012300.00   \n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760  48748200.00   \n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000  50985100.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  Raw_return  \n",
       "Day                                   \n",
       "1995-01-03  1.806930e+08   -0.012333  \n",
       "1995-01-04  3.069230e+08    0.021770  \n",
       "1995-01-05  3.015330e+08   -0.010584  \n",
       "1995-01-06  3.537580e+08   -0.009476  \n",
       "1995-01-09  3.985190e+08   -0.023035  \n",
       "...                  ...         ...  \n",
       "2024-09-24  4.427953e+07    0.041547  \n",
       "2024-09-25  5.166981e+07    0.011589  \n",
       "2024-09-26  5.246691e+07    0.036131  \n",
       "2024-09-27  4.806126e+07    0.028850  \n",
       "2024-09-30  1.167773e+08    0.080637  \n",
       "\n",
       "[7223 rows x 8 columns]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new=data['1995-01':'2024-09'].copy()\n",
    "data_new['Close']=pd.to_numeric(data_new['Close'])\n",
    "data_new['Preclose']=pd.to_numeric(data_new['Preclose'])\n",
    "#计算000001上证指数日收益率 两种:\n",
    "data_new['Raw_return']=data_new['Close']/data_new['Preclose']-1\n",
    "data_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data=data_new.resample('ME')['Raw_return'].apply(lambda x:(1+x).prod()-1).to_frame()\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.005695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.018086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.008281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.148387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000642</td>\n",
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       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.001441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.011045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RV\n",
       "month               \n",
       "1995-01-31  0.005695\n",
       "1995-02-28  0.018086\n",
       "1995-03-31  0.013378\n",
       "1995-04-30  0.008281\n",
       "1995-05-31  0.148387\n",
       "...              ...\n",
       "2024-05-31  0.000915\n",
       "2024-06-30  0.000642\n",
       "2024-07-31  0.001441\n",
       "2024-08-31  0.000705\n",
       "2024-09-30  0.011045\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "market_varince=data_new.resample('ME').apply(\n",
    "    {\n",
    "        'Raw_return': lambda x: sum(x**2)\n",
    "    }\n",
    ")\n",
    "market_varince.reset_index(inplace=True)\n",
    "market_varince.rename(columns={'Day':'month','Raw_return':'RV'},inplace=True)\n",
    "market_varince.set_index('month',inplace=True)\n",
    "market_varince"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "      <td>24.1</td>\n",
       "      <td>0.005695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "      <td>22.4</td>\n",
       "      <td>0.018086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "      <td>21.3</td>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "      <td>20.7</td>\n",
       "      <td>0.008281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "      <td>20.3</td>\n",
       "      <td>0.148387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.000915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.000642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.001441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.000705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.011045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return   cpi        RV\n",
       "1995-01-31   -0.131631  24.1  0.005695\n",
       "1995-02-28   -0.023694  22.4  0.018086\n",
       "1995-03-31    0.177803  21.3  0.013378\n",
       "1995-04-30   -0.103552  20.7  0.008281\n",
       "1995-05-31    0.207922  20.3  0.148387\n",
       "...                ...   ...       ...\n",
       "2024-05-31   -0.005801   0.3  0.000915\n",
       "2024-06-30   -0.038684   0.2  0.000642\n",
       "2024-07-31   -0.009656   0.5  0.001441\n",
       "2024-08-31   -0.032849   0.6  0.000705\n",
       "2024-09-30    0.173908   0.4  0.011045\n",
       "\n",
       "[357 rows x 3 columns]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data=pd.merge(Month_data,inflation,left_index=True,right_index=True,how='inner')\n",
    "reg_data=pd.merge(reg_data,market_varince,left_index=True,right_index=True,how='inner')\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "TO_t = \\sum_{d= 1}^{D_t}(\\frac{\\sum_i^{N_d} TradeMoney_{i,d,t}}{\\sum_i^{N_d} FloatingValue_{i,d,t}})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R_t = a + b * TO_{t-1} + \\epsilon_t\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Stkcd</th>\n",
       "      <th>month</th>\n",
       "      <th>Rank</th>\n",
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       "      <th>ret</th>\n",
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       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>000001</td>\n",
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       "      <td>20.0</td>\n",
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       "      <td>20.869546</td>\n",
       "      <td>21.473968</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>000001</td>\n",
       "      <td>1991-05-31</td>\n",
       "      <td>2</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-0.128345</td>\n",
       "      <td>1.016010e+09</td>\n",
       "      <td>1.859497e+09</td>\n",
       "      <td>20.739149</td>\n",
       "      <td>21.343572</td>\n",
       "      <td>0.007087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>000001</td>\n",
       "      <td>1991-06-30</td>\n",
       "      <td>3</td>\n",
       "      <td>23.0</td>\n",
       "      <td>-0.119551</td>\n",
       "      <td>9.007350e+08</td>\n",
       "      <td>1.648521e+09</td>\n",
       "      <td>20.618722</td>\n",
       "      <td>21.223144</td>\n",
       "      <td>0.001155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>000001</td>\n",
       "      <td>1991-07-31</td>\n",
       "      <td>4</td>\n",
       "      <td>16.0</td>\n",
       "      <td>-0.137013</td>\n",
       "      <td>7.828100e+08</td>\n",
       "      <td>1.432695e+09</td>\n",
       "      <td>20.478401</td>\n",
       "      <td>21.082823</td>\n",
       "      <td>0.000230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>000001</td>\n",
       "      <td>1991-08-31</td>\n",
       "      <td>5</td>\n",
       "      <td>15.0</td>\n",
       "      <td>-0.417680</td>\n",
       "      <td>6.748338e+08</td>\n",
       "      <td>1.346275e+09</td>\n",
       "      <td>20.329977</td>\n",
       "      <td>21.020607</td>\n",
       "      <td>0.072087</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>752023</th>\n",
       "      <td>605599</td>\n",
       "      <td>2023-08-31</td>\n",
       "      <td>24</td>\n",
       "      <td>23.0</td>\n",
       "      <td>-0.027103</td>\n",
       "      <td>7.955351e+09</td>\n",
       "      <td>1.054667e+10</td>\n",
       "      <td>22.797111</td>\n",
       "      <td>23.079076</td>\n",
       "      <td>0.134479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>752024</th>\n",
       "      <td>605599</td>\n",
       "      <td>2023-09-30</td>\n",
       "      <td>25</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0.071030</td>\n",
       "      <td>8.530295e+09</td>\n",
       "      <td>1.130889e+10</td>\n",
       "      <td>22.866890</td>\n",
       "      <td>23.148855</td>\n",
       "      <td>0.137497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>752025</th>\n",
       "      <td>605599</td>\n",
       "      <td>2023-10-31</td>\n",
       "      <td>26</td>\n",
       "      <td>17.0</td>\n",
       "      <td>-0.048696</td>\n",
       "      <td>8.125488e+09</td>\n",
       "      <td>1.077222e+10</td>\n",
       "      <td>22.818272</td>\n",
       "      <td>23.100237</td>\n",
       "      <td>0.086762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>752026</th>\n",
       "      <td>605599</td>\n",
       "      <td>2023-11-30</td>\n",
       "      <td>27</td>\n",
       "      <td>22.0</td>\n",
       "      <td>-0.027956</td>\n",
       "      <td>7.908417e+09</td>\n",
       "      <td>1.048444e+10</td>\n",
       "      <td>22.791193</td>\n",
       "      <td>23.073159</td>\n",
       "      <td>0.062795</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>752027</th>\n",
       "      <td>605599</td>\n",
       "      <td>2023-12-31</td>\n",
       "      <td>28</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0.103358</td>\n",
       "      <td>8.735632e+09</td>\n",
       "      <td>1.158111e+10</td>\n",
       "      <td>22.890676</td>\n",
       "      <td>23.172641</td>\n",
       "      <td>0.082049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>685834 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Stkcd      month  Rank  Freq       ret  floatingvalue    totalvalue  \\\n",
       "0       000001 1991-04-30     1  20.0       NaN   1.157520e+09  2.118487e+09   \n",
       "1       000001 1991-05-31     2  24.0 -0.128345   1.016010e+09  1.859497e+09   \n",
       "2       000001 1991-06-30     3  23.0 -0.119551   9.007350e+08  1.648521e+09   \n",
       "3       000001 1991-07-31     4  16.0 -0.137013   7.828100e+08  1.432695e+09   \n",
       "4       000001 1991-08-31     5  15.0 -0.417680   6.748338e+08  1.346275e+09   \n",
       "...        ...        ...   ...   ...       ...            ...           ...   \n",
       "752023  605599 2023-08-31    24  23.0 -0.027103   7.955351e+09  1.054667e+10   \n",
       "752024  605599 2023-09-30    25  20.0  0.071030   8.530295e+09  1.130889e+10   \n",
       "752025  605599 2023-10-31    26  17.0 -0.048696   8.125488e+09  1.077222e+10   \n",
       "752026  605599 2023-11-30    27  22.0 -0.027956   7.908417e+09  1.048444e+10   \n",
       "752027  605599 2023-12-31    28  21.0  0.103358   8.735632e+09  1.158111e+10   \n",
       "\n",
       "            sizef      sizet      to_v  \n",
       "0       20.869546  21.473968  0.000506  \n",
       "1       20.739149  21.343572  0.007087  \n",
       "2       20.618722  21.223144  0.001155  \n",
       "3       20.478401  21.082823  0.000230  \n",
       "4       20.329977  21.020607  0.072087  \n",
       "...           ...        ...       ...  \n",
       "752023  22.797111  23.079076  0.134479  \n",
       "752024  22.866890  23.148855  0.137497  \n",
       "752025  22.818272  23.100237  0.086762  \n",
       "752026  22.791193  23.073159  0.062795  \n",
       "752027  22.890676  23.172641  0.082049  \n",
       "\n",
       "[685834 rows x 10 columns]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross=pd.read_csv('datasets/cross_section2023.csv')\n",
    "from pandas.tseries.offsets import MonthEnd\n",
    "cross['month']=pd.to_datetime(cross['month'],format='%Y-%m-%d')+MonthEnd(1)\n",
    "cross['to_v']=pd.to_numeric(cross['to_v'])\n",
    "cross['floatingvalue']=pd.to_numeric(cross['floatingvalue'])\n",
    "cross=cross.dropna(subset=['to_v','floatingvalue'])\n",
    "cross['Stkcd']=cross['Stkcd'].apply(lambda x:'{:0>6}'.format(x))\n",
    "cross"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>to</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>0.001785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.019217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.038486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>0.014105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>0.014399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-31</th>\n",
       "      <td>0.262355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>0.202123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-31</th>\n",
       "      <td>0.203982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-30</th>\n",
       "      <td>0.274035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>0.235034</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>397 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  to\n",
       "month               \n",
       "1990-12-31  0.001785\n",
       "1991-01-31  0.019217\n",
       "1991-02-28  0.038486\n",
       "1991-03-31  0.014105\n",
       "1991-04-30  0.014399\n",
       "...              ...\n",
       "2023-08-31  0.262355\n",
       "2023-09-30  0.202123\n",
       "2023-10-31  0.203982\n",
       "2023-11-30  0.274035\n",
       "2023-12-31  0.235034\n",
       "\n",
       "[397 rows x 1 columns]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "turnover=pd.DataFrame(cross.groupby('month').apply(\n",
    "    lambda x:\n",
    "    np.average(x['to_v'],weights = x['floatingvalue'])\n",
    ",include_groups = False))\n",
    "turnover.rename(columns = {0:'to'}, inplace = True)\n",
    "turnover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "      <th>to</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "      <td>24.1</td>\n",
       "      <td>0.005695</td>\n",
       "      <td>0.096488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "      <td>22.4</td>\n",
       "      <td>0.018086</td>\n",
       "      <td>0.104393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "      <td>21.3</td>\n",
       "      <td>0.013378</td>\n",
       "      <td>0.400929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "      <td>20.7</td>\n",
       "      <td>0.008281</td>\n",
       "      <td>0.325164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "      <td>20.3</td>\n",
       "      <td>0.148387</td>\n",
       "      <td>0.721733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-08-31</th>\n",
       "      <td>-0.052009</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001546</td>\n",
       "      <td>0.262355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.003013</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000884</td>\n",
       "      <td>0.202123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-10-31</th>\n",
       "      <td>-0.029483</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>0.001068</td>\n",
       "      <td>0.203982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-11-30</th>\n",
       "      <td>0.003611</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.000497</td>\n",
       "      <td>0.274035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.018067</td>\n",
       "      <td>-0.3</td>\n",
       "      <td>0.001009</td>\n",
       "      <td>0.235034</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>348 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return   cpi        RV        to\n",
       "1995-01-31   -0.131631  24.1  0.005695  0.096488\n",
       "1995-02-28   -0.023694  22.4  0.018086  0.104393\n",
       "1995-03-31    0.177803  21.3  0.013378  0.400929\n",
       "1995-04-30   -0.103552  20.7  0.008281  0.325164\n",
       "1995-05-31    0.207922  20.3  0.148387  0.721733\n",
       "...                ...   ...       ...       ...\n",
       "2023-08-31   -0.052009   0.1  0.001546  0.262355\n",
       "2023-09-30   -0.003013   0.0  0.000884  0.202123\n",
       "2023-10-31   -0.029483  -0.2  0.001068  0.203982\n",
       "2023-11-30    0.003611  -0.5  0.000497  0.274035\n",
       "2023-12-31   -0.018067  -0.3  0.001009  0.235034\n",
       "\n",
       "[348 rows x 4 columns]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data=pd.merge(reg_data,turnover,left_index=True,right_index=True,how='inner')\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 换手率图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
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   "source": [
    "fig=plt.figure(figsize=(12,5))\n",
    "ax=fig.add_subplot(1,1,1)\n",
    "ax.plot(\n",
    "    'to',\n",
    "    '.-r',\n",
    "    linewidth=1,\n",
    "    data=reg_data['2000':]\n",
    ")\n",
    "plt.title('Monthly turnover rate of Chinese Stock Market')\n",
    "plt.xlabel('Month')\n",
    "plt.ylabel('Turnover rate')\n",
    "\n",
    "\n",
    "data_format=mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator(1))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "plt.show;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "fig=plt.figure(figsize=(12,5))\n",
    "ax=fig.add_subplot(1,1,1)\n",
    "ax.plot(\n",
    "    'RV',\n",
    "    '.-r',\n",
    "    linewidth=1,\n",
    "    data=reg_data['2000':]\n",
    ")\n",
    "plt.title('Monthly variance of Chinese Stock Market')\n",
    "plt.xlabel('Month')\n",
    "plt.ylabel('Variance')\n",
    "\n",
    "\n",
    "data_format=mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator(1))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "plt.show;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R_t=a-\\gamma*RV_{t-1}+\\epsilon_t\n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "E_{t-1}(RV_t)\n",
    "$$\n",
    "\n",
    "\n",
    "$$\n",
    "R_t=a-\\gamma*TO_{t-1}+\\epsilon_t\n",
    "$$\n",
    "\n",
    "\n",
    "1. 我们找到更好地预测波动率的指标\n",
    "2. 模型错了！\n",
    "\n",
    "\n",
    "$$\n",
    "R_t=a+\\gamma*RV_{t-1}+\\mathbf{B}*\\mathbf{X}_{t-1}+\\epsilon_t\n",
    "$$\n",
    "\n",
    "\n",
    "模型设定错误：丢失变量问题（Ommited Variables Problem）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Solarize_Light2', '_classic_test_patch', '_mpl-gallery', '_mpl-gallery-nogrid', 'bmh', 'classic', 'dark_background', 'fast', 'fivethirtyeight', 'ggplot', 'grayscale', 'seaborn-v0_8', 'seaborn-v0_8-bright', 'seaborn-v0_8-colorblind', 'seaborn-v0_8-dark', 'seaborn-v0_8-dark-palette', 'seaborn-v0_8-darkgrid', 'seaborn-v0_8-deep', 'seaborn-v0_8-muted', 'seaborn-v0_8-notebook', 'seaborn-v0_8-paper', 'seaborn-v0_8-pastel', 'seaborn-v0_8-poster', 'seaborn-v0_8-talk', 'seaborn-v0_8-ticks', 'seaborn-v0_8-white', 'seaborn-v0_8-whitegrid', 'tableau-colorblind10']\n"
     ]
    },
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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Change the figure style\n",
    "# list the figure style\n",
    "print(plt.style.available)\n",
    "#plt.style,use('ggplot')\n",
    "# #使用默认的画图风格\n",
    "plt.style.use('ggplot')#ggplot可换为default\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax1= fig.add_subplot(1,1,1)\n",
    "#(x，x，x)这里前两个表示几*几的网格，最后一个表示第几子图\n",
    "\n",
    "\n",
    "ax1.plot(reg_data['RV'],\n",
    "         color='red',\n",
    "         marker='.',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=6,\n",
    "         alpha=0.4,\n",
    "         label='Market Variance')\n",
    "ax1.set_xlabel('Month')#设置横坐标标签\n",
    "ax1.set_ylabel('Return') #设置纵坐标标签\n",
    "#ax1.legend(loc=2) #设置图例在左上方\n",
    "ax1.set_title(\"China Stock Market Turnover and Variance\")#给整张图命名\n",
    "\n",
    "#设置轴的日期显示格式\n",
    "data_format =mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "#转置x轴的日期显示格式\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax2=ax1.twinx()#twinx()函数表示共享x轴\n",
    "ax2.plot(reg_data['to'],\n",
    "         color='blue',\n",
    "         marker='o',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=2,\n",
    "         alpha=0.7,\n",
    "         label='Tornover')\n",
    "ax2.set_ylabel('Turnover')#设置右边纵坐标标签\n",
    "#ax2.legend(loc=1)#设置图例在右上方\n",
    "\n",
    "\n",
    "#change the legend into one box\n",
    "lines,labels=ax1.get_legend_handles_labels()\n",
    "lines2,labels2=ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Solarize_Light2', '_classic_test_patch', '_mpl-gallery', '_mpl-gallery-nogrid', 'bmh', 'classic', 'dark_background', 'fast', 'fivethirtyeight', 'ggplot', 'grayscale', 'seaborn-v0_8', 'seaborn-v0_8-bright', 'seaborn-v0_8-colorblind', 'seaborn-v0_8-dark', 'seaborn-v0_8-dark-palette', 'seaborn-v0_8-darkgrid', 'seaborn-v0_8-deep', 'seaborn-v0_8-muted', 'seaborn-v0_8-notebook', 'seaborn-v0_8-paper', 'seaborn-v0_8-pastel', 'seaborn-v0_8-poster', 'seaborn-v0_8-talk', 'seaborn-v0_8-ticks', 'seaborn-v0_8-white', 'seaborn-v0_8-whitegrid', 'tableau-colorblind10']\n"
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       " </g>\n",
       " <defs>\n",
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       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Change the figure style\n",
    "# list the figure style\n",
    "print(plt.style.available)\n",
    "#plt.style,use('ggplot')\n",
    "# #使用默认的画图风格\n",
    "plt.style.use('ggplot')#ggplot可换为default\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax1= fig.add_subplot(1,1,1)\n",
    "#(x，x，x)这里前两个表示几*几的网格，最后一个表示第几子图\n",
    "\n",
    "\n",
    "ax1.plot('RV',\n",
    "         color='red',\n",
    "         marker='.',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=6,\n",
    "         alpha=0.4,\n",
    "         label='Market Variance',\n",
    "         data=reg_data['2000':])\n",
    "ax1.set_xlabel('Month')#设置横坐标标签\n",
    "ax1.set_ylabel('Return') #设置纵坐标标签\n",
    "#ax1.legend(loc=2) #设置图例在左上方\n",
    "ax1.set_title(\"China Stock Market Turnover and Variance\")#给整张图命名\n",
    "\n",
    "#设置轴的日期显示格式\n",
    "data_format =mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "#转置x轴的日期显示格式\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax2=ax1.twinx()#twinx()函数表示共享x轴\n",
    "ax2.plot('to',\n",
    "         color='blue',\n",
    "         marker='o',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=2,\n",
    "         alpha=0.7,\n",
    "         label='Tornover',\n",
    "         data=reg_data['2000':])\n",
    "ax2.set_ylabel('Turnover')#设置右边纵坐标标签\n",
    "#ax2.legend(loc=1)#设置图例在右上方\n",
    "\n",
    "\n",
    "#change the legend into one box\n",
    "lines,labels=ax1.get_legend_handles_labels()\n",
    "lines2,labels2=ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.180\n",
      "Model:                            OLS   Adj. R-squared:                  0.177\n",
      "Method:                 Least Squares   F-statistic:                     18.23\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):           2.66e-05\n",
      "Time:                        15:05:56   Log-Likelihood:                 1136.1\n",
      "No. Observations:                 288   AIC:                            -2268.\n",
      "Df Residuals:                     286   BIC:                            -2261.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0005      0.001      0.581      0.561      -0.001       0.002\n",
      "lto            0.0131      0.003      4.270      0.000       0.007       0.019\n",
      "==============================================================================\n",
      "Omnibus:                      163.950   Durbin-Watson:                   1.027\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              843.343\n",
      "Skew:                           2.437   Prob(JB):                    7.42e-184\n",
      "Kurtosis:                       9.821   Cond. No.                         6.52\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lto']=reg_data['to'].shift(1)\n",
    "reg_data['lRV']=reg_data['RV'].shift(1)\n",
    "reg_data['cpi']=reg_data['cpi'].shift(1)\n",
    "\n",
    "\n",
    "model_forecast_rv=smf.ols('RV~lto',data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags':6})\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.371\n",
      "Model:                            OLS   Adj. R-squared:                  0.369\n",
      "Method:                 Least Squares   F-statistic:                     54.39\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):           1.79e-12\n",
      "Time:                        15:05:56   Log-Likelihood:                 1174.4\n",
      "No. Observations:                 288   AIC:                            -2345.\n",
      "Df Residuals:                     286   BIC:                            -2337.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0017      0.000      4.919      0.000       0.001       0.002\n",
      "lRV            0.6095      0.083      7.375      0.000       0.447       0.771\n",
      "==============================================================================\n",
      "Omnibus:                      116.912   Durbin-Watson:                   2.234\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              460.052\n",
      "Skew:                           1.714   Prob(JB):                    1.26e-100\n",
      "Kurtosis:                       8.157   Cond. No.                         193.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_forecast_rv=smf.ols('RV~lRV',data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags':6})\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.399\n",
      "Model:                            OLS   Adj. R-squared:                  0.395\n",
      "Method:                 Least Squares   F-statistic:                     31.63\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):           3.94e-13\n",
      "Time:                        15:05:56   Log-Likelihood:                 1180.8\n",
      "No. Observations:                 288   AIC:                            -2356.\n",
      "Df Residuals:                     285   BIC:                            -2345.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0004      0.001      0.689      0.491      -0.001       0.001\n",
      "lRV            0.5251      0.091      5.787      0.000       0.347       0.703\n",
      "lto            0.0057      0.002      2.780      0.005       0.002       0.010\n",
      "==============================================================================\n",
      "Omnibus:                      124.981   Durbin-Watson:                   2.196\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              502.264\n",
      "Skew:                           1.844   Prob(JB):                    8.60e-110\n",
      "Kurtosis:                       8.315   Cond. No.                         227.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_forecast_rv=smf.ols('RV~lRV+lto',data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.002\n",
      "Method:                 Least Squares   F-statistic:                    0.1190\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):              0.730\n",
      "Time:                        15:05:56   Log-Likelihood:                 354.24\n",
      "No. Observations:                 288   AIC:                            -704.5\n",
      "Df Residuals:                     286   BIC:                            -697.2\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0086      0.009      0.995      0.320      -0.008       0.026\n",
      "fitted_RV     -0.7635      2.214     -0.345      0.730      -5.102       3.575\n",
      "==============================================================================\n",
      "Omnibus:                       14.630   Durbin-Watson:                   1.737\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               37.298\n",
      "Skew:                          -0.028   Prob(JB):                     7.96e-09\n",
      "Kurtosis:                       4.762   Cond. No.                         306.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data_new=reg_data['2000':].copy()\n",
    "reg_data_new['fitted_RV']=model_forecast_rv.fittedvalues\n",
    "\n",
    "\n",
    "model_forecast_return=smf.ols('Raw_return~fitted_RV',data=reg_data_new).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_forecast_return.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.023\n",
      "Model:                            OLS   Adj. R-squared:                  0.019\n",
      "Method:                 Least Squares   F-statistic:                     3.585\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):             0.0593\n",
      "Time:                        15:05:56   Log-Likelihood:                 357.35\n",
      "No. Observations:                 288   AIC:                            -710.7\n",
      "Df Residuals:                     286   BIC:                            -703.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0138      0.009     -1.571      0.116      -0.031       0.003\n",
      "lto            0.0634      0.033      1.893      0.058      -0.002       0.129\n",
      "==============================================================================\n",
      "Omnibus:                       21.077   Durbin-Watson:                   1.839\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               50.287\n",
      "Skew:                          -0.314   Prob(JB):                     1.20e-11\n",
      "Kurtosis:                       4.949   Cond. No.                         6.52\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_to=smf.ols('Raw_return~lto',data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC',\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_to.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>to</th>\n",
       "      <th>RV</th>\n",
       "      <th>cpi</th>\n",
       "      <th>lto</th>\n",
       "      <th>lRV</th>\n",
       "      <th>lcpi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.317318</td>\n",
       "      <td>1.860277</td>\n",
       "      <td>0.029683</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-06-30</th>\n",
       "      <td>0.071041</td>\n",
       "      <td>1.310464</td>\n",
       "      <td>0.007385</td>\n",
       "      <td>-0.4</td>\n",
       "      <td>1.860277</td>\n",
       "      <td>0.029683</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-09-30</th>\n",
       "      <td>-0.009310</td>\n",
       "      <td>1.021229</td>\n",
       "      <td>0.005522</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.310464</td>\n",
       "      <td>0.007385</td>\n",
       "      <td>-0.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-12-31</th>\n",
       "      <td>0.085501</td>\n",
       "      <td>0.743491</td>\n",
       "      <td>0.003498</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.021229</td>\n",
       "      <td>0.005522</td>\n",
       "      <td>-0.4000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-03-31</th>\n",
       "      <td>0.018954</td>\n",
       "      <td>0.544915</td>\n",
       "      <td>0.006189</td>\n",
       "      <td>2.7</td>\n",
       "      <td>0.743491</td>\n",
       "      <td>0.003498</td>\n",
       "      <td>1.3000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>0.021448</td>\n",
       "      <td>0.737284</td>\n",
       "      <td>0.005982</td>\n",
       "      <td>6.5</td>\n",
       "      <td>0.830530</td>\n",
       "      <td>0.004817</td>\n",
       "      <td>5.7304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-03-31</th>\n",
       "      <td>0.059432</td>\n",
       "      <td>0.716085</td>\n",
       "      <td>0.002786</td>\n",
       "      <td>4.9</td>\n",
       "      <td>0.737284</td>\n",
       "      <td>0.005982</td>\n",
       "      <td>7.7000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-06-30</th>\n",
       "      <td>-0.021632</td>\n",
       "      <td>0.797789</td>\n",
       "      <td>0.003526</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.716085</td>\n",
       "      <td>0.002786</td>\n",
       "      <td>6.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "      <td>0.699933</td>\n",
       "      <td>0.003941</td>\n",
       "      <td>-0.2</td>\n",
       "      <td>0.797789</td>\n",
       "      <td>0.003526</td>\n",
       "      <td>4.9000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "      <td>0.713052</td>\n",
       "      <td>0.002575</td>\n",
       "      <td>-0.7</td>\n",
       "      <td>0.699933</td>\n",
       "      <td>0.003941</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>96 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return        to        RV  cpi       lto       lRV    lcpi\n",
       "2000-03-31    0.317318  1.860277  0.029683 -0.5       NaN       NaN     NaN\n",
       "2000-06-30    0.071041  1.310464  0.007385 -0.4  1.860277  0.029683     NaN\n",
       "2000-09-30   -0.009310  1.021229  0.005522  1.3  1.310464  0.007385 -0.5000\n",
       "2000-12-31    0.085501  0.743491  0.003498  1.3  1.021229  0.005522 -0.4000\n",
       "2001-03-31    0.018954  0.544915  0.006189  2.7  0.743491  0.003498  1.3000\n",
       "...                ...       ...       ...  ...       ...       ...     ...\n",
       "2022-12-31    0.021448  0.737284  0.005982  6.5  0.830530  0.004817  5.7304\n",
       "2023-03-31    0.059432  0.716085  0.002786  4.9  0.737284  0.005982  7.7000\n",
       "2023-06-30   -0.021632  0.797789  0.003526  1.0  0.716085  0.002786  6.5000\n",
       "2023-09-30   -0.028603  0.699933  0.003941 -0.2  0.797789  0.003526  4.9000\n",
       "2023-12-31   -0.043575  0.713052  0.002575 -0.7  0.699933  0.003941  1.0000\n",
       "\n",
       "[96 rows x 7 columns]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qreg_data=reg_data['2000':].copy()\n",
    "Qreg_data=Qreg_data.resample('QE').apply(\n",
    "    {'Raw_return':lambda x:(1+x).prod()-1,\n",
    "     'to':lambda x:sum(x),\n",
    "     'RV':lambda x:sum(x),\n",
    "     'cpi':lambda x:sum(x)}\n",
    ")\n",
    "Qreg_data['lto']=Qreg_data['to'].shift(1)\n",
    "Qreg_data['lRV']=Qreg_data['RV'].shift(1)\n",
    "Qreg_data['lcpi']=Qreg_data['cpi'].shift(2)\n",
    "Qreg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.080\n",
      "Model:                            OLS   Adj. R-squared:                  0.070\n",
      "Method:                 Least Squares   F-statistic:                     8.056\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):            0.00557\n",
      "Time:                        15:05:57   Log-Likelihood:                 54.844\n",
      "No. Observations:                  95   AIC:                            -105.7\n",
      "Df Residuals:                      93   BIC:                            -100.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0630      0.031     -2.043      0.044      -0.124      -0.002\n",
      "lto            0.0863      0.030      2.838      0.006       0.026       0.147\n",
      "==============================================================================\n",
      "Omnibus:                        7.906   Durbin-Watson:                   1.843\n",
      "Prob(Omnibus):                  0.019   Jarque-Bera (JB):               13.927\n",
      "Skew:                           0.211   Prob(JB):                     0.000946\n",
      "Kurtosis:                       4.827   Cond. No.                         4.14\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model_to_q=smf.ols('Raw_return~lto',data=Qreg_data).fit(\n",
    "    voc_type='HAC',\n",
    "    cov_kwds={'maxlags':2}\n",
    ")\n",
    "print(model_to_q.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.019\n",
      "Model:                            OLS   Adj. R-squared:                  0.008\n",
      "Method:                 Least Squares   F-statistic:                     1.797\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):              0.183\n",
      "Time:                        15:05:57   Log-Likelihood:                 50.852\n",
      "No. Observations:                  94   AIC:                            -97.70\n",
      "Df Residuals:                      92   BIC:                            -92.62\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0368      0.022      1.649      0.103      -0.008       0.081\n",
      "lcpi          -0.0035      0.003     -1.340      0.183      -0.009       0.002\n",
      "==============================================================================\n",
      "Omnibus:                       17.458   Durbin-Watson:                   1.663\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               25.329\n",
      "Skew:                           0.835   Prob(JB):                     3.16e-06\n",
      "Kurtosis:                       4.917   Cond. No.                         13.1\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model_cpi_q=smf.ols('Raw_return~lcpi',data=Qreg_data).fit(\n",
    "    voc_type='HAC',\n",
    "    cov_kwds={'maxlags':2}\n",
    ")\n",
    "print(model_cpi_q.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.094\n",
      "Model:                            OLS   Adj. R-squared:                  0.074\n",
      "Method:                 Least Squares   F-statistic:                     4.733\n",
      "Date:                Wed, 13 Nov 2024   Prob (F-statistic):             0.0111\n",
      "Time:                        15:10:30   Log-Likelihood:                 54.595\n",
      "No. Observations:                  94   AIC:                            -103.2\n",
      "Df Residuals:                      91   BIC:                            -95.56\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0418      0.036     -1.166      0.247      -0.113       0.029\n",
      "lto            0.0857      0.031      2.746      0.007       0.024       0.148\n",
      "lcpi          -0.0032      0.003     -1.254      0.213      -0.008       0.002\n",
      "==============================================================================\n",
      "Omnibus:                        8.001   Durbin-Watson:                   1.880\n",
      "Prob(Omnibus):                  0.018   Jarque-Bera (JB):               13.075\n",
      "Skew:                           0.271   Prob(JB):                      0.00145\n",
      "Kurtosis:                       4.745   Cond. No.                         27.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model_to_q=smf.ols('Raw_return~lto+lcpi',data=Qreg_data).fit(\n",
    "    voc_type='HAC',\n",
    "    cov_kwds={'maxlags':2}\n",
    ")\n",
    "print(model_to_q.summary())"
   ]
  }
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